I doubt it, but ask HR. You could transfer locally to a different building, assuming there were positions available. However, you can't do anything (transfer locally or switch from twi to sunrise) until you've been employed for at least a year. That I heard from HR in my hub.
No, you cannot. But you can apply for an equivalent shift with FedEx Ground -- neither FedEx nor UPS typically prohibits inside PT, non-managerial employees from working for each other, although it's best to check with your HR manager first.
Transfers may be considered after 6 months in some locations. Ask your HR rep.